Question

triangle xyz was translated up 2 and right 3 units, creating triangle cab. which relationship between the parts of the two triangles must be true?
∠x≅∠a
zx≅ca
yz≅ab
∠z≅∠c

Explanation:

Step1: Recall translation property

Translation is a rigid - motion. Rigid - motions preserve side lengths and angle measures. Corresponding parts of translated figures are congruent. When $\triangle XYZ$ is translated to $\triangle CAB$, the vertices correspond as follows: $X$ corresponds to $C$, $Y$ corresponds to $A$, and $Z$ corresponds to $B$.

Step2: Analyze angle - angle congruence

For angles, $\angle X$ corresponds to $\angle C$, $\angle Y$ corresponds to $\angle A$, and $\angle Z$ corresponds to $\angle B$. For sides, $\overline{XY}$ corresponds to $\overline{CA}$, $\overline{YZ}$ corresponds to $\overline{AB}$, and $\overline{ZX}$ corresponds to $\overline{BC}$.

Answer:

$\overline{YZ}\cong\overline{AB}$